# Energy supplied by circuit

1. Aug 24, 2009

### smith5753

1. The problem statement, all variables and given/known data

For the element shown below, v(t) = ½ t Volts and i(t) = 12t-4t2 Amps.

a)Find the instantaneous power p(t) as a function of time.

b)Find the energy supplied (this value can be negative or positive for each range) to the element for the following three time ranges:

0 < t < 3, 3 < t < 4, 0 < t < 4, those are less than or equal to.

2. Relevant equations

There is a picture of the circuit that show that it satisfies the Passive Sign Convention.

P(t) = V(t) i(t)

w= the integral of P(t)

3. The attempt at a solution

for part a. I multiplied the given V times the i and found p(t) to = 6t^2 - 2t^3 watts.

for part b. I attempted to take the integral of P(t) from the first point listed; 0 < t < 3

I dont understand the integration. Do i integrate from infinitie to 0, then from 0 to 3, and then from 3 to infinitie?? im so lost at this point.

2. Aug 24, 2009

### rock.freak667

Re: Physics/Circuits

Just integrate form 0 to 3

EDIT: also if you have infinity in the limits, the polynomial will tend to infinity as t→ inf.